Abstract
This paper contains exact expressions for the complete class of uncountably many globally optimal affine Nash equilibrium strategies for a two-stage two-person nonzero-sum game problem with quadratic objective functionals and with dynamic information for both players. Existence conditions for each of these Nash equilibrium solutions are derived and it is shown that a recursive Nash solution is not necessarily globally optimal. Cost-uniqueness property of the derived Nash strategies is investigated and it is proven that the game problem under consideration admits a unique Nash cost pair if and only if it can be made equivalent to either a team problem or a zero-sum game. It is also shown that existence conditions of a globally optimal Nash solution will be independent of the parameters characterizing the nonuniques of the Nash strategies only if the game problem can be made equivalent to a team problem.
Original language | English (US) |
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Pages (from-to) | 48-54 |
Number of pages | 7 |
Journal | IEEE Transactions on Automatic Control |
Volume | 21 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1976 |
Externally published | Yes |
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering